The objective of this paper is to identify factors which limit the ability of Zambian farmers to increase Maize productivity and/or diversify their crop mix. Both may enable wealth accumulation, investments, and further expansion. Specifically, we link variations in agricultural decisions, practices, and outcomes, to variations in the tightness of the different constraints. We model crop production decisions as having recursive structure. Initially, farmers decide on land allocation among the different crops, based on their information set at planting time. Then, as new information (weather, market conditions) is revealed, farmers can change output by influencing the yield. This recursive structure enables to separate the effects of the constraints on the different stages of production. We therefore conduct estimation in two stages: we first estimate the fraction of land allocated to Maize as a dependent variable that is censored from below and from above, so that its predicted value is necessarily between zero and one. The yield of Maize is estimated in the second stage as a linear function of calculated land allotment (to avoid simultaneity bias) and the other state variables. Environmental and demographic variables also serve as explanatory variables in each stage. The first-stage results indicate that crop diversification can be promoted by rural road construction, developing markets for agricultural products, increasing the availability of seeds, draught animals, and farm machines, increasing women's farm work participation, and increasing the size of landholdings. Specialization in Maize can be promoted by increasing the availability of credit, fertilizers, hired permanent workers, and irrigation knowledge, and improving the timeliness of input delivery. The second-stage results show that the yield of Maize is inversely related to the area of Maize cultivated and to the operator's age, and is lower in female-headed farm households. Maize productivity can be improved by increasing the availability of seeds, fertilizers, labor, draught animals, machines, and credit.